Essential Concepts in Economics, Budgeting, and Statistics
Zero-Based Budgeting
Zero-based budgeting is a method in which all expenses must be justified for each new period. The budget starts at a zero base, and every function within the organization is analyzed for its needs and costs. Therefore, budgets are built based on what is required for the upcoming period, regardless of the previous budget size.
Taxes
Taxes are a compulsory contribution to state revenue. It is mandatory to pay taxes, which are levied by the government on workers’ income and business
Read MoreEssential Geometry Theorems and Properties
Quadrilaterals
- The sum of the interior angles of a quadrilateral is 360°.
- Properties of a parallelogram:
- Opposite sides are equal.
- Opposite angles are equal.
- Consecutive angles are supplementary (sum = 180°).
- Diagonals bisect each other.
- A diagonal divides it into two congruent triangles.
- Conditions for a parallelogram:
- Both pairs of opposite sides are equal.
- Both pairs of opposite angles are equal.
- Diagonals bisect each other.
- One pair of opposite sides is equal and parallel.
- Mid-Point Theorem: The line segment
Solving Polynomial Equations: Descartes and Cardan Methods
1. Nature of Roots: Descartes’s Rule of Signs
Find the nature of the roots for the equation: x⁴ + 2x² + 3x – 2 = 0
Applying Descartes’ Rule of Signs
Given the function: f(x) = x⁴ + 2x² + 3x – 2
Signs of coefficients: +, +, +, –
Count sign changes:
- + to + (No change)
- + to + (No change)
- + to – (1 change)
Therefore, there is exactly one positive real root.
Replace x with -x:
f(-x) = (-x)⁴ + 2(-x)² + 3(-x) – 2 = x⁴ + 2x² – 3x – 2
Signs: +, +, -, –
Count sign changes:
- + to + (No change)
- + to – (1 change)
Refractive Index Determination: Glass Slab and Prism Experiments
Experiment 6: Refractive Index Determination
Part 1: Refractive Index of a Glass Slab (Pin Method)
Aim
To determine the refractive index of a glass slab material using the pin method.
Apparatus and Materials
Glass slab, drawing board, drawing pins, hairpins, paper, scale, and protractor.
Theory
The refractive index, n, of glass with respect to air is defined by Snell’s Law:
n = sin i / sin r
where i is the angle of incidence and r is the angle of refraction.
A graph plotted with sin r along the X-axis and
Read MoreEssential Excel Formulas and Functions Reference
Quick Reference: Excel Formulas
- Adding many cells: =SUM
- Adding 2 cells: + or –
- Finding typical value: =AVERAGE
- Finding true middle: =MEDIAN
- Finding smallest: =MIN
- Finding largest: =MAX
- Counting numbers: =COUNT
- Counting text or anything: =COUNTA
- Applying rule/condition: =IF
- Calculating loan payment: =PMT
- Summarizing multiple sheets: 3D SUM
- Testing different scenarios: Goal Seek / Data Table
- Multiplying by fixed %: Absolute reference ($)
1. Mathematical & Statistical Functions
These are the workhorses of Excel
Read MoreCore Epidemiology Concepts: Definitions, History, and Measures
Lectures 1–2 – Intro to Epidemiology
Key Definitions:
Epidemiology: study of frequency, distribution, determinants of health/disease in populations + application to control.
Frequency: how often events occur (counts, proportions, rates).
Distribution: patterns by person/place/time.
Determinants: factors influencing occurrence (host/agent/environment).
Historical Figures (name + contribution):
Edward Jenner: cowpox → smallpox vaccine (1st vaccination).
James Lind: scurvy + citrus trial.
Percival Pott: